Can shadows connect black hole microstructures?

We investigate the relationship between shadow radii (photosphere radii) and black hole microstructures for a static spherically symmetric black hole and confirm their close connection. As a concrete analysis, we take the Reissner-Nordstr$\mathrm{\ddot{o}}$m AdS black hole surrounded by perfect fluid dark matter (RN AdS black hole surrounded by PFDM) as an example. We calculate the Ruppeiner thermodynamic scalar curvature and shadow radius (photosphere radius) for the specific model. On the one hand, we find that the greater density of the perfect fluid dark matter makes black hole molecules more likely have attractive interactions. On the other hand, we provide the support to our general investigation that the shadow radii (photosphere radii) indeed connect the microstructures of this model.

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